Definition

Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $a \in R$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

Let $\map { {B_\epsilon}^-} a$ be the closed $\epsilon$-ball of $a$.

In $\map { {B_\epsilon}^-} a$, the value $a$ is referred to as the center of the closed $\epsilon$-ball.

Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.